Apparatus for eliminating mechanical vibrations in aerial cables



MASON 2,907,811

W. P. APPARATUS FOR ELIMINATING MECHANICAL VIBRATIONS IN AERIAL CABLES 4 Sheets-Sheet 1 Oct. 6, 1959 Filed Feb. 26, 1954 INVENTOR y W R MASON 4T7 RNEV Oct. 6, 1959 w. P. MASON 2,907,811

APPARATUS FOR ELIMINATING MECHANICAL VIBRATIONS IN AERIAL CABLES Filed Feb. 26, 1954 4 Sheets-Sheet 2 5 FIG. 4

' Q INVENTOR By W. R MASON A 7' TORNEV Oct. 6, 1959 w. P. MASON 2,907,811

APPARATUS FOR ELIMINATING MECHANICAL VIBRATIONS IN AERIAL CABLES 4 Sheets-Sheet 3 Filed Feb. 26, 1954 FIG. 6

INVENTOR By W P. MASON ATTORNEY Oct. 6, 1959 w. P. MASON 2,907,811

APPARATUS FOR ELIMINATING MECHANICAL VIBRATIONS IN AERIAL CABLES Filed Feb 26, 1954 4 Sheets-Sheet 4 FIG. 8

INVENTOR y n. R MASON %emu' AT RNEY United States Patent Application February 26, 1954, Serial No. 412,770 2 Claims. Cl. 174-42 This inventionmrelates to apparatus for eliminating harmful effects of mechanical vibration in the spans of an aerial: cable system; I Moreparticularly, it relates to apparatus for freely transmitting theyertical mechanical vibrationsarriving at the end of a cable span, either to an absorbing or dissipative mechanical terminating member or to adjacent spans of the aerial cable system. The establishingcof vertical standing'waves of substantial'amplitude on any span is, thereby, effectively inhibited. I Low frequency vertical vibrations are established in theispans of an aerial cable system by unbalanced air pressures generated by winds of evenvery moderate velocity. If the end of'the span is rigidly'supported, in accordance with the substantially universal practice of the prior art, or if'themechanical impedance of the sup for the vibrational frequencies involved is substantially dififere'ntfrom that of the cable span, the vibrations are reflected back into the span from the support and a substantial. vertical standing wave is established on the span: which tends to increase in amplitude under the ccntinuing influence of the wind. The phenomena is known to those skilledin the art as dancing of the cable. Very substantial amplitudes may be established .and rupt ure ofjvitalportionsof the cable, particularlyat or near a where smaller branching-cables thesupp'ort, by fatigue phe nomena are not infrequent.

In accordance with the present invention, if the prior art types of supports at each end of each span are eliminated by substituting supporting means whlch are also mechanical band passwave filters having-a mechanical impedance substantially matching that of the spans of cable and capable of freely transmitting the vibrational energy from'each" span into the next successive adjacent span, at either end of a span the vibrational energy of all the spans will be distributed in a randommanner throughout a plurality of spans. Interference phenomena will thensubstantially reduce the amplitude of the vibrations irifeachjsp an and effectively inhibit theestablishing of largestanding waves. Also, because of the mechanical impedance match. and the free transmission of the vibraticnal energy through the points of support from spanto sp an,ifatigue-and rupture of portions of the cable at and near the points of support are effectively eliminated.

Alternatively, any of the mechanical wave filter sup- -porting means of the invention may have one endconnected to 'a mechanical energy absorbing device, or termination? as it is called in electrical circuits, such as a dashp'otf"prony brake, or the like, the mechanical impedance of"whichfisubstantially matches that of the filter. The end of'the cable spanis then connected to the'other end of the mechanical filter and the vibratory energy. of the" cable span will be freely transmitted through the filter to the energy absorbing deviceand be absorbed thereby, substantially no energy being refieeted hack into the cable span. This alternative arrangementigofcourse, particularly appropriate for use at the end'of the last span-bf 'an aerial cable system where there is 'no adjacent span to which vibrational energy may be transmitted. Itma'y also be desirable to employ 2,907,811 eer? Q FBYIQ QJ .5, such arrangement'where' successive spans are'of sub stantially different lengths or mechanical characteristics or are connectedto a large trunk cable system, etc. a. i

Investigation of the vibrational" phenomena involved has revealed that, to be effective, 'themechanicalfband pass filter employed to support. and"interconnect the successive spansmechan'icallyfor to terminate anyspan mechanically) must not only have'a' sufiiciently' wide pass-band that it .will pass a number of the" lower harmonics of the fundamental vibrational frequency of the cable span but it must also substantially match'the mechanicalimpedance' of the cable span at these'vibrational frequencies of the span. It should be particularly noted that even though the filter did noniinally transmit a very wide frequency band it' might nevertheless reflect substantially allenergy applied to its inputif its charac teristic mechanical impedance differs grossly from that of the cable span at the frequencies of the applied energy.

To recapitulate, thewave filter, cable supporting means must both freely transmit several low harmonics ofthe fundamental frequency of vibration of the cable" span (usuallyat' least the second, third and fourth harmonics of the fundamental frequency) and substantially matchthe characteristic mechanical irn edanceofthe cablespan at these frequencies. u I

The frequencies of vertical vibration of a-scable' span and its characteristic" mechanical impedance'willboth vary appreciably with changes in temperature. For ex ample,-in a 300 foot span of a widelyused typeof cable the frequencies of vibrationa'n'd its characteristic mechan= ical impedance may vary approximately ten percent with the temperature variationsto be expected throughout the year in numerouslocalities in which aerial cables are employed. It is, therefore, further necessary that the mechanical filters of the invention havean even wider pass-band of frequencies within which they substantially match'the mechanical impedance of the cable span and freely pass the lower harmonics of thefund'amental frequency for the complete ranges of variation of vibration frequency and impedance, respectively, corresponding to the temperature variations likely to be encountered in the locality in which any particular aerial cable is installed.

Theserious inadequacies of-the' majority of'such prior art cable supporting arrangements as do'em'pl'oy movable mechanicalsupports, can usuallybe readily traced to either a lack of even an approximate match of theme chanical impedance of the cable span or an insufiiciently wide frequency pass-band, or both, so that the stronger harmonic frequencies of vertical vibrationare not freely transmitted from span to span. Obviously, a support mechanically resonant at a single frequency'can be effective only at that frequency and even at that frequency its characteristic impedance may differ so greatly from that of the cable span that a substantial portion .of the vertical vibratory energy is reflected back into the span in which it originated rather than being passed freely to the successive spans. Moreover, singly resonant structures cannot readily be designed-to follow changes in the vibrationfrequency or impedance of the cableresulting from temperature changes.

As is well understood by those skilledin the art, prop erly designed wave filters- (electrical or mechanicalfcan be considered as vibratory systems. exhibiting, inetfect, a continuous resonance throughout the entire range of frequencies which are freely transmitted through the filter. Furthermore, a properly designed wave filter (either electrical or mechanical) which freely transmits a wide band of frequencies can also provide substantially predetermined varying characteristic impedance over a major portion of the wide frequency range which it freel'yltransmits. The mechanical band-pass wave filter supports ,of the invention are thus, obviously, readily adaptable to provide both free transmission and a substantially matching impedance over a broad range of frequencies, as requiredto obtain the objectives of the presentinventiom- I 1 An interesting exposition, including illustrative photographs, of the action of a specific mechanical band-pass wave -.filter-isgiven, for example, .in the article entitled Filters. in Action by C. E. Lane, published September l9..33g;in vol. 12, No. 1, of the Bell Laboratories Record, pages 2 through-.7, inclusive. While the filter described by Lane is, obviously, not adaptedfor the purposes of the present invention, the article illustrates pictorially the generic phenomena encountered with mechanical wave filters. j

A primary object of the invention, accordingly, is the elimination of harmful effects of mechanical vibration inthe spans-of an aerial cable system. .;Another; object is to facilitate the free transmission of mechanical vibrational energy from each span of an aerial cablesystemto adjacentspans of the system. Another object is to provide for the substantially complete and reflectionless absorption of vertical mechanical vibratory energy at the end of a cable span.

.A further object is to provide band-pass, mechanical wave filter, cable-supporting means having suitable characteristic'impedances and sufliciently wide pass-bands to freely'transmitthe principal harmonics of the fundamental frequency of vibrations arising in the spans of anaerial cable system throughout the entiretemperature range .of the locality in which the cable system is located. 1

A still further object-is to provide simple, convenient and economicalmechanical band-pass filter structures for use in supporting'the'spans of, aerial cable systems.

.Other. and further objects and features of the invention will become apparent during the course of the following description of specific illustrative embodiments of the principles of the invention and from the appended claimswr' a A few of the numerous and varied forms which the devices of'the invention may take are shown in the accompanying drawings in which:

I Fig. 1 illustrates a portion of a multispan aerial telephone cable system typical of those with which the mechanical band-pass wave filter supports of the invention are intended to be used; 7

Fig. .2 is a schematic diagram of an analogous type ofelectrical band-pass wave filter corresponding closely to the specific illustrative mechanical band-pass wave filters illustrated in Figs. 3 and 4; Y

Fig. 3 is a diagrammatical illustration of one possible assembly of mechanical'elernents which can be arranged, proportioned and interconnected to constitute a mechanical band-pass wave filter for use as an interspan supportingarrangement in aerial cable systems in accordance with the principles of the invention;

' Fig.4 illustrates a particularly simple, convenient and economical form of mechanical, band-pass, wave filter, span supporting arrangement operating in accordance withfthe principles of the invention;

Fig. Sis an end view of the principal elements of the filter structure illustrated in Fig. 4;

Figs. 6and 7 illustrate the combination of a mechanical band-pass wave filter of the type illustrated by Figs.v 4 and 5 with a vibratory mechanical energy absorbin'gmean'sor termination connected to the output of the wave-filter; and

Figs. .8 and -9-illustrate a still further'form of mechanic'al, band-pass, wave filter, cable supporting arrangement embodying the principles of the present invention.

Several otherspecifically different forms of mechanicalfiltering arrangements, embodying certain of the genericprinciples and suitable for use in cable supportmaltiesmay require.

' ing arrangements of the present invention, are shown in the companion application of R. N. Thurston, Serial No. 412,888, being filed February 26, 1954, concurrently with the present application, and assigned to applicants assignee. This application matured as Patent 2,852,595 granted September 16, 1958. Numerous and varied other specific forms of mechanical wave filters suitable for use as cable supporting means in accordance with the principles of the present invention can, obviously, be readily devised by those skilled in the art. Applicants book entitled Electromechanical Transducers and Wave Filters, Second Edition, published by- D. Van; Nostrand Co., Inc., 250 Fourth Avenue, New York 3, New York, 1948, discusses and illustrates the general-principles involved in the design of mechanical wave filters.

In more detail in Fig. l, a conventional aerial telephone cable system is illustrated and comprises a cable 10 supported at a plurality of substantially equal intervals by supporting means '11, aflixedto wooden telephone poles 12. In prior art cable systems the supporting means 11 are usually substantially rigid with the result that mechanical vibration originating in a span is reflected from the support back into the span in which it originated and standing waves of substantial amplitude are quickly established. In accordance with the principles of the present invention, supporting means which do not reflect any substantial amount of the vibratory energy back into the span in which it originated are employed an'dthe tendency to build up large amplitude standing waves on any span is thus largelyeliminated. For a typical installation, the distance between poles maybe in the-order'of 300 feet, the distance being occasionally varied as theparticular terrain orfother local abnor- A frequently used type of telephone cable includes a steel supporting strandand-a plurality ofinsulated pairs ofhighly conductive'wire, the latter being encased in a combined metal and'plastic sheath; Usually paper, or some similar material "is employed to insulate the individual wires of the-cable and the sheath is relied upon to exclude moisture which would destroy the elfectiveness ofsu'chinsulation. The strand" may in many instances be itself composed of a plurality of smaller steel strands twisted together.

The sheath is bound to or otherwise supported by the supporting steel stran d at short intervals so as to'relieve the sheath and electrical conductors of the cable of substantially all tensile stress. Thecombination of cable andsupporting strand for a frequently used cable of the above mentioned type weighs approximately 0.57 pound per linear foot. This particular cable is'usually hung so that for a 300 foot span, the s tee'l.stran is under a tension in the order of between l5 00'and 2000 pounds and the center of the span has a sag of substan tially inches below the pointsof support on thepoles at the ends of the span (assuming that both end sup ports are in'substantially'the same horizontal plane).

' "The serious consequences which may result from .dancing or vertical vibration of the cable, as described in detail above are readily apparent since it may result I tinuing action of the wind.

in the rupture of the cable sheath or even of the steel supporting strand. Should the strand become ruptured, the full tension must be assumed by the cable itself and rupture of both the sheath and the'conductors may then result. In extreme cases of cable dancing even the supporting poles have been damaged by the violence of the standing waves which have been built up by the condesignated "0.27 pound per foot, the total mass periniit length is 0.0l78slug per foot. The propagation velocity, assuming a tension on the steel strand of 1550 pounds, is 294 feet per second. The characteristic impedance Z of the cable and strand under these conditions is 5.25 slugs per second or 5.25 pound seconds per foot.

The sag, and hence the tension, the propagation velocity, and the characteristic impedance all change appreciably with temperature as has beenpreviously indicated.

stantially match the cable impedance and must freely transmit at least the above no'ted group of harmonic: frequencies for all values that they may assume over the range of temperatures encountered in the locality in which the aerial cable system is installed. 7

In analyzing the specific illustrative forms of mechanical filters employed in the arrangements of the present invention and particularly those illustrated in Figs. 3, 4 and 8 of the accompanying drawings, reference will be made to an analogous form'of band-pass electrical wave filter, shown in electrical schematic diagram form in Fig. 2 of the accompanyingdrawings.

This electrical filteris also shown as filter number 9 of Table I at pages 52 and 53 of applicants above-mentioned: book entitled Electromechanical Transducers and Wave Filters,-. Second Edition, and its' impedance and transmission, characteristics are indicated; Applicants abovementioned book and the publications cited therein .may be referred to for complete detailed explanations ofthe theory, design and construction of both electrical and mechanical Wave filter structures of numerous and varied forms and construction. In more detail in Fig. 2, a single full section of a conventional type of electrical band-pass wave filter, terminated in mid-series arms at each end, is illustrated in electrical schematic diagram form. It comprises two like series arms each consisting of an inductance 14, also /2L and acapacitance 16, also designated as 2C and a single shunt branch or arm intermediate the two series arms, as shown,'the shunt ing a single capacitor 18, also designated C As is well known to those skilled in ath e art, the literal designations of the elements indicate that for each of the series arms the value of inductance is one half and the value of the capacitance is double'that which would be found in the series armof a full section of the same type of filter, if terminated, for: example, in mid-shunt, or otherwise, at each end respectively.- Assuming that an input voltage designated E is applied to'tlie left terminals of the filter section shown-in Fig. 2 and results in an "output voltage, designated E 1 (across an electrical load connected to the right-hand terminals of the section), a current of i will flow in the left-hand mesh and'a re sulting current of i will flow in the right-hand mesh. The mesh equations for 'the structurea're:

radians, i.e., it gis21r'tiines the frquency'of the applied:

signal.)

The following filter relations hold:

branch comprisfilter which is known as the i6 wg=21rf where is the-lowest frequency passed'by the lower cutoff frequency.

, =2 irf where f is the highest frequency passed the filter which is lcnown as the upper cutoff frequency.

Z; is the image impedance.

I),,,= wiao4') v(6) where 'Z is the maximum value of the image impedance' in the transmitted band and occurs,

for the specific filter illustrated by Fig. "2, at substantially the mid-frequency of the transmitted band. The symbol Z; is the conventional symbol employed for image impedance in filter design formulae. The subscript I employed as part of this symbol stands for -image and is in no way related to the symbol 1 used independently to denote moment of inertia. I e

From" Equations 3, 4 and 6 the nominal values of the elements of the filter of Fig.2 may be obtained.

max

q max hI :In .general, as" is explained in my above mentioned book, electrical inductance is analogous to mass and electrical capacitance is analogous to compliance, respectively, of the elements of a corresponding mechanical wave filter adaptable to 'supportan aerial cable in accordance with the principles of the invention is illustrated. This e qm .tnet a ta y .z d ltic luj t e springs 28 and 36, each having a stiffness k, the substantially identical weights 30 and 34, each having a mass M, and the length of the cable 32 between the weights 30 and 34. Forthe purpose of this analysis, the just-mentioned section of cable is treated as a flexible string under tension characterized by a particular stiffness, the weight of this section of cable being considered as contributing half its weight to each 'of the identical weights 30' and 34. As shown in Fig. 3, spring 36 is deflected or extended morethan spring 28 which would j correspond to an instant'at-which an upwardly directed force-from the left span had 'decre ased the extension of spring 28 and the tension of the cable section between weights 30 and 34 had not yet correspondingly raised weight '34. Whenat rest, i.e., in the position of static equilibrium, springs 28 and 36 would be extended equally.

The upper ends of the springs 28 and 36 are supported, with a predetermined spacing'lj between them, by the fixed rigid member 22. Member 22 can appropriately be either of steel or of wood of suitable cross-sectional area, proportioned and shaped to aiford a substantially fixed rigid support. It is "bolted rigidly to pole 20 by means of bolts 26 and steel clamping; plate 24.

Weights 30 and 34 are supporte'd' by the lower ends of springs 28 and 36,j respectively, as shown.

; "-.:The.cable 32*is securely fastened by any appropriate :c'lamping means to the weights 30 and, the length of 1117 ;the cable 32 between the weights being such that springs 28 andfifiare; when at rest, maintained in substantially vertical positions. The horizontal rigid member 22 should be substantially parallel to the cable 32 and in the same vertical plane therewith. The portion of ;;5

that the vibratory energy in the. cablespan to the leftexerts at a given instant an upwardly directed force F .on the weight 3 0.. and that as, ,a result of this force, an instantaneous downwardly directed force of F is exerted .bythg weight 34 on the cable span to the right of weight 34. The direction of F will, as iswell known to those.

skilled} in the art, depend upon the location of the frequency of the'vibration being transmitted within the transmitting band of the filter ln the vicinity of the upper portion of the transmitting band for an upwardly directed force F F will be downwardly directed while in the .;lower: portion of the band,vF will also be upwardly directed. See article Filters in Action by C. E. Lane, mentioned above. It is further assumed that y and y are the respective vertical displacements of weights 30 and 34 from theirrespective static equilibriumpositions.

Assuming further, a substantially sinusoidal steady state vertical oscillationof the end of the cable span to the left of weight '30 we may write for the velocities of vertical movement of weights 30 and 34, respectively. (The dot above y and y signifies the first derivative with respect to time and two dots in Equations 11 and 12, below, signify the second derivative with -respecttotimeJ which for steady-state oscillations of frequency a: may written respectively as Comparison ot 'EquatiOnslS and l4lab rve with the mesh Equations 1 and Z of; the electrical wave filter illusg vl/ic corresponds to 2 C '1 M corresponds to /2 1 g'corresponds to C v corresponds to i "v corresponds to i F v corresponds to E v Fi corresponds to E The element values- L C C or Ztheir respective rnechanical analogues determine the cut-ofifrequenciesg,

whence .18 :wA,'vB,:al1:d the characteristic impedance at any frequency w, Z 00) is determined inaccordance with therelations '.iEfi: 1G1 M r 7 V -1' 1 4" k' 2r 1 r L1 (0'1 c2)- Mr 6 '17 The fmaximurnvalue of Z occurs at fiisf fgand'is i ZIQ fB-4A)' The static deflection B fofithe spring due to the weight oi the mass M'satisfiesthe'relation' h where g is the symbol representing gravitational acceleration whence V 4 i I i are k 1,2 I If L, is to be less than say 0.8 cycle per second, then w Z5.3 sect and I I 32.2 6 2- 1.27 feet In addition to the weight of the' massM, the spring must support the weight of a half span ofcable which is approximately pounds.v Thedeflection due to the static weight oflthe cable is.'-

n a a whence where W=weight per span.

From Equation 15,

Fm n uaaens 15 and 16, 20,

1ml l' 4T ff From Equations 18 and 20, J V I i zl =zlid%atflifffidj (22 whence V 1 e 2 a. 47rfAZImx fA v 3) Suppose f =3 cycles per second and f, ==0.8 cycle per second then f /f, =3.75. Assuming that a 2 to l im pedance mismatch is permissible at midband, then I vchanical, wave filter,

in accordance with the principlesof the present inven* ,-tion, is shownin Figs. 4 and 5 of the accompanying I.;- -In Fig. 4 the pole bolt 54 and nut 55,

ber.5.2, which extends in a direction parallel to the cable .70 and generally in the same vertical plane ,with the support the steel bar 60 ends as shown. The bearings 56,58 permit free rotation of ..ba r 60 about its longitudinal, axis but prevent other 7 .62 and 64 are fi mly attached a .by keys 61 and -63,,respectively, shown in Fig. 5, and at and 64.

V clamps 71 and 73) an spective cable span supported by each of the arms 62, 64

To lower v6,, to 1.5 feet with these same cutoffs would require 1 percent of the incident energy and would obviously not be satisfactory. 1 a

The large static defleotion required to obtain'a wide band with reasonably close'impedance matching makes this arrangement impractical for use with'the typical cable described above. However for a considerably lighter cable thevfilter of Fig. 3 would prove feasible.

For the relatively heavy cable described in detail above, a particularly simple and economical band-pass, me-

cable supporting means operating drawings. 'Fig. 5 is an end view of the major elements comprising the filter structure ofFig. 4, and shows the angular relation of the end arms '62, 64, of the structure more clearly.

50 has firmly attached thereto, by a a horizontal rigid supporting memcable 70. Member 52 carries'bearings'56 and 58 which at positions near its respective movement of bar 60.

At each-end of bar 60, substantially identical rigid. arms to bar 60 asfor example the respectiveangles indicated in Fig. 5 for the arms 62 d The cable 70 is held firmly'by stud-bolts 66, nuts 78 and clamps 73 and 71 on the ends of arms 64 and 62, respectively, details of the clamping arrangements being also shown in Fig.5. A protective member 66 on the end of each of the arms 62 protective member 68 around the cable at each point'of clamping are preferably provided to avoid damaging the cable sheath. Rubberized fabrics suitable foruse as protective members are wellknown to those-skilled in the art.

Between clamps 73 and 71 a loop of the cable 70 is left" under substantially no tension and, except ;for its contribution to the eifective weights of the arms 64 and 62,

respectively, the loop plays no part in the filtering action of the over-all structure of Figs. .4 and 5. 1

The mechanical band-pass wave filterfca'ble support of.

Fig. ,4 is designed so that arms 62 and 64 are substantially rigid,; each having (with thecontribution of substantially half the weight of the cable loop between intertia I. The tension of the recan be balanced by connecting the end of each of these arms to the center point of rod 60 orto a closely.adja-.

cent point on supporting member 52 by a short flexible steel cable, without sensibly atfecting the over-all operation of the mechanical filter structure. Such short cables filter operation. H p

The bar 60, assuming an instantof no, cable vibration are not shown on .Fig. 4 since they do notenter into the (i.e., the static equilibrium position), is under a constant torque produced by; the Weights of the cable spans to the; left of arm 64-and to the right of arm 62and the effective weights of the arms themselves. The bar 60 thus afiords a coupling or mutual torsional stiffness between the arms 64 and 62. A ,stiffness effectively in series with each of the arms 64 and 6,2 is aflforded by the tendency 0111 75 1 and 64' and a ring-shaped in the respective 510 gravity vtorestorefthe structure to its static equilibrium position whenever vibrational forces cause itto assume some other position. The underlying principle involved is ofcourse that which permits a timepiece or clock to employ' a balance wheel and'res'toring spring in place of a pendulum and the restoring force of gravity, or vice versa.

of bar 60 as shown. The distances a and b will be re- 1; ferred .to

as the horizontal and .vertical projections, re-

. spectively,o f each of the arms 62-and 64.

Instantaneous displacements 641and.62 from the static equilibrium position are indicated by broken lines 77 and 79 at angles 0 and 0 respectively, in Fig.5.

The resulting vertical displacements of the ends of arms 64and 62 are designated as y and y respectively, for

purposes of the analysis given hereinunder.

Designating the ends of arms 64 and 62 by the numbers l and 2, respectively, the vertical vibrational forces which the cable spans exert on the ends 1 and 2 are assumed to act purely'in vertical planes parallel to each other and to the fixed longitudinal (horizontal) axis of bar 60, i.e., the axis of rotation of bar 60. Since the vertical vibration of the cable has been found to be mainly responsible for damage to the cable, the above assumption is deemed appropriate and therefore only the vertical components are considered in computing the moments about'the fixed horizontal axis of bar 60.

The symbols to be e pl'oyed in the analysisiof the structure of Figs. 4 and 5 are as follows:

=weight per span of cable and supporting strand F =vertical (upward) component of force exerted on.

end j by cable and strand, where j is taken successively to refer to ends 1 and 2 respectively.

where F,-=alternating part of F 05-=angulaf displacement of endjfrom its initial static load equilibrium position y,- 'vertical displacement of endJ-jfrom its initial static load equilibrium position 2= zr- T (variable part of T ,..Egfl

The equations of motion for the mount are I 1 :11 (Thedouble dots above Oindicate the-second derivative wi ht t i I 1 f a @(1' ms e2) v v 27) If we expressthe functions of as power s' eries, and neglect powers'of (9 higher than the first, and also neglect ha; in comparison with a, then the expressionsfor T and 06 02- sin m sin 9 2 i These equations may be put in the form of the usual steady' state 'mesh equations for the circuit ofvFig. 2 by writing" z- V 1 (i =A,-e where i== /-l v (32) 95 37:; and

These substitutions lead to By comparisonwiththe mesh equations for the circuit of Fig. 2, the correspondences betweencthe mechanical quantities of the device of Fig.4 and theielectri'cal quantities of the structure of Fig 2" are as follows:

L corresponds to I 2C corresponds to Z/Wb c corresponds toll k i E corresponds to F a E corresponds toF a i corresponds to 9' i correspondsto- By making use of these=correspondences i'n-the relations listed for the structure of Fig. 2, the following relations are obtained- 4 Whenthe structure is properly-terminated to prevent reflections, "I 1 4 Z1.=,= 2 39 01 Since b ah/a, and b s /a F1 F3 i Z 7 92/1 fly:

' The significant advantage of this arrangement over .the preceding one (Fig. 3) is that the stifiness corresponding to 1/2C is not required to support the strand, but only --'to provide a stable equilibrium position for the structure.

. The degree of 'stability is determined by the value of b. Equation "3 5 shows that b is proportional to the square of -.thel'ower cutoff, T Hence, this cutofi can be lowered to any desired value, but only by sacrificing static stabili- 'ty for the structure; There is a practical lower limit for b, and hence for f5. 1

The stiflness coupling, k, is not a limiting parameter, since almost any desired value of k can be built into the structure by selection of appropriate values for the length, diameter and resilience of the bar 60. In a typical case of a filter fojr the typical cable described above bar was of mild steel having a diameter of 0.86 inch and a'length of 5 feet. I This arrangement has the disadvantage that the cable spans exert a torque (applied at the ends of arms 6 2,6'4) about a vertical axis. Thistorquecan, however, normally be resisted adequately by the supportingtpole. For heavy cables a more-elaborate tower of steel or the like maybe-required to adequately resist this vertical torque, or in some instances two like cables with their respective supports can contribute mutually opposed torques to compensate for each other.

- Let us investigate the possibilitiejof this filter by again assuming a 2 to l impedance mismatch at 'midband with ."cutoffsat 0.8 cycle per second and 3 'cycles' per second.

:51" he matching impedance for this filter is obtained from 7 Equation 4 by setting F /y 5.25 slugs/sec. Thus, for a 2 to mismatch at midband, g

V i V I slug ft? second Then Z =42 slug ftF/sec, and

blime-i=2 feet,

'; from Equation 38, the required moment of inertia is .The corresponding value of b is 0.9 foot. The moment of inertia can be kept considerably lower than 3 slwg ft resulting 'eitherin a wider pass band, or in a better' 'imqThus, f could be raised to'7.3 cycles per second. The corresponding value of b would be about '2 inches. In

this case, only 57 foot pounds of-work could produce a w degree rotation of the structure. In some situations a larger'value of b is therefore desirable. A larger value can readily be'obtained either-:by raising I; thus lowering 1 Before ending this discussion, it willbe instructive'to considersome limitingcases of this filter, 'With b=0,

the (statically neutral) structure is a lowpass filter with the structurewould be a rigid, inertia-less lever, with perfect transmission (like'a direct-connection) 'forall frequencies. "If the 's tructurevva's perfectly rigid (k 'oo) but with stability and inertia, there would be perfecttrans- 'missiononly at the-frequency" for which PWb/ZI. -'Since' stability and inertia are ne cessary, the advantage as) 5* of building 'conipliande into' the structure and designing it as a band-pass filter is apparent since nearly perfect transmission and satisfactory impedance relations can be obtained over a wide band of frequencies. This would be impossible with a perfectly rigid structure.

In Figs. 6 and 7 the use of one form of resistive termination for a mechanical bandpass cable supporting wave lter of the invention is illustrated. For convenience, the filter shown is that described above in detail in connection with Figs. 4 and 5, corresponding designation numbers being applied in Figs. 6 and 7 to like features of the two arrangements.

In Fig. 6 the cable 78 is clamped to the end of arm 64 by clamp 73 and bolts 78 as described above, the cable extending to the left of arm 64 as a span in the order of 300 feet long to a pole and supporting arrangement such as is illustrated in Figs. 4 and 5, for example. To

the right of arm 64 of Fig. 6 the cable is, for example, led

down the pole Silt to a terminal station, a sufilcient loop being left between arm 64 and the uppermost cable to pole fastener 182 that free normal movement of arm 64 is not impeded.

In Fig. 6 the end of arm 62 of the mechanical filter cable supporting means is connected by a pivot joint 82 and rod 80 to the piston 86, shown in Fig. 7, of dashpot 84. Dash-pot 84 is supported on trunnions 88 in the U-shaped bracket 92. Bracket 92 is supported on arm 94, one end of which arm is fastened to pole 50 by lag-screw 108. The other end of arm 94 is supported by a steel brace 96, a bolt 99 serving to both hold the bracket 92 on the arm 94 and to fasten the upper end of brace 96 to arm 94, as shown. Lag-screw 98 secures the lower end of brace 96 to the pole 58.

As is shown more clearly in the partial end view of Fig. 7, the piston 86 of dash-pot 84 is provided with a number of holes and the dash-pot 84 is filled with a viscous fluid 90 so that motion of piston 86 requires that appreciable energy be expended in forcing the piston to move through the fluid. As described, the dash-pot arrangement constitutes a mechanical, resistive, or energy dissipative, termination for the filter comprising arms 64, 62 and bar 60. The termination is proportioned to substantially match the characteristic mechanical impedance of the filter over its pass band of mechanical vibrational frequencies and thus will absorb with substantially no reflection all vibratory energy transmitted through the filter from cable 70 to arm 62. Obviously such a resistive termination could also be applied to any other suitable form of mechanical wave filter cable support. Alternatively, a mechanism of the well known prony-brake type could be employed as a resistive termination for any of the mechanical wave filter cable supports of the invention.

In Figs. 8 and 9, top and side views, respectively, of a modification of the mechanical wave filter cable supporting arrangement of Figs. 4 and are shown. The arrangement illustrated by Figs. 8 and 9 is designed to avoid the torque about a vertical axis involved in the arrangement of Figs. 4 and 5, while retaining substantially all of the advantages of the latter arrangement.

The arrangement illustrated in Figs. 8 and 9 has the bar 60 supported for rotary motion about its longitudinal axis by bearings 56 and 58 which in turn are mounted on the rigid arm 52 supported by the pole 50 as for the arrangement of Figs. 4 and 5.

The arms 164 and 162 extend in both directions from bar 60 and are keyed thereto by keys 61 as shown. Arms 164 and 162 are counterweighted by weights 170 which can be moved along their respective arms to compensate for the weight of the cable span on the opposite end of the arm in each instance. Set screws 172 are tightened to hold weights 170 in position after proper adjustments have been made. As shown in the view of Fig. 8, the cable 70 passes directly from the lower or front end of arm 164 to the corresponding end of arm 162 and thence 14 to the next successive span of cable. The straight line arrangement of the cable from span to span thus achieved enables the steel strand of the section of cable between arms 164 and 162. to assume the tension of the spans and thus further relieve the filter arms of a stress which may become of troublesome magnitude for the heavier telephone cables. Features of Figs. 8 and 9 bearing the same designation numbers respectively as features of Figs. 4 and 5 are as described in connection with the last mentioned figures. Obviously, it can readily be demonstrated by those skilled in the art that the structure of Figs. 8 and 9 is substantially equivalent to that of Figs. 4 and 5 and is a mechanical band-pass filter structure analogous to the electrical wave filter represented by the schematic diagram of Fig. 2.

Numerous other and further arrangements involving the principles of the invention and within the spirit and scope thereof can readily be devised by those skilled in the art.

What is claimed is:

1. Mechanical filtering means for supporting the adjacent ends of a successive pair of cable spans of an aerial cable system, said filtering means comprising an elongated bar of resilient material, rigidly supported bearing means supporting said bar in a horizontal position for free rotation about its longitudinal axis, a first rigid arm attached rigidly to a first end of said bar at an angle of substantially degrees with respect to the longitudinal axis of said bar, a second rigid arm attached rigidly to the other end of said bar at an angle of substantially 90 degrees with respect to the longitudinal axis of said bar, the plane including the longitudinal axes of said first arm and said bar being at an angle diifering by a predetermined small amount from 180 degrees with respect to the plane including the longitudinal axes of said second arm and said bar, means at the free end of said first arm for securely fastening the end of one of said pair of cable spans, means at the free end of said second arm for securely fastening the end of the other of said pair of cable spans, the moments of inertia about the longitudinal bar axis of said first and second arms, the compliance of said bar and the gravitational restoring forces on said arms constituting a mechanical band-pass filter which freely passes a predetermined band of vibrational frequencies including several low harmonics of the fundamental frequency of transverse vibration of said cable spans, the characteristic mechanical impedance of said filter over said band of frequencies substantially matching a predetermined characteristic mechanical impedance said last mentioned impedance being that of the cable spans with which said filter is to be employed.

2. Cable interspan supporting means comprising a resilient rod, fixed bearing means supporting the rod horizontally for rotation about its longitudinal axis, a pair of rigid arms attached to opposite ends of the rod, respectively, the arms being substantially at right angles to the rod and at an angle of approximately degrees with respect to each other, and cable holding means on the free end of each arm, the masses of the arms and the resilience of the rod being proportioned to constitute a mechanical wave filter passing a predetermined frequency band of transverse vibrational energy, the filter having a mechanical impedance substantially matching the mechanical impedance of the cable for said energy.

4 7 References Cited in the file of this patent UNITED STATES PATENTS 1,666,681 Burgess Apr. 17, 1928 2,727,085 Tornquist et a1. Dec. 13, 1955 2,790,843 Gordon Apr. 30, 1957 FOREIGN PATENTS 554,712 Germany July 14, 1932 

